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Novel Use of Predictive Marginals in Interpretation of Complex Models

*Barnali Das, WestatKarla Mcpherson, WestatAndrea Sedlak, Westat

Keywords: Predictive marginals, logistic regression, interpretation

Data from the 4th National Incidence Study of Child Abuse and Neglect were analyzed using logistic regression to examine Black/White differences in maltreatment. Obtaining final models and coefficients is often the stopping point for regression but, for non-statisticians, it is hard to interpret each regression coefficient as being adjusted for other predictors in the model. The technique of predictive marginals can help. Here, we created a hypothetical population of an equal number of Black and White children in every cell specified by other predictors in the model, equalizing the race distribution across all model factors. Marginal probabilities by race were obtained by applying the model-based probabilities of maltreatment in each cell to the hypothetical population and calibrating to the estimated probability of maltreatment computed from the raw data. These marginal probabilities are standardized for any race-related differences in the population distributions of the other factors in the model and are more understandable than the regression coefficients, clearly demonstrating the race differences that remain after all the other predictors are taken into account.